molstar
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A comprehensive macromolecular library.
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JavaScript
/**
* Copyright (c) 2017-2020 mol* contributors, licensed under MIT, See LICENSE file for more info.
*
* @author David Sehnal <david.sehnal@gmail.com>
* @author Alexander Rose <alexander.rose@weirdbyte.de>
*/
/*
* This code has been modified from https://github.com/toji/gl-matrix/,
* copyright (c) 2015, Brandon Jones, Colin MacKenzie IV.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*/
import { EPSILON, equalEps } from './common';
import { degToRad } from '../../misc';
function Mat4() {
return Mat4.zero();
}
/**
* Stores a 4x4 matrix in a column major (j * 4 + i indexing) format.
*/
(function (Mat4) {
function zero() {
// force double backing array by 0.1.
var ret = [0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
ret[0] = 0.0;
return ret;
}
Mat4.zero = zero;
function identity() {
var out = zero();
out[0] = 1;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = 1;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 1;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
Mat4.identity = identity;
function setIdentity(mat) {
mat[0] = 1;
mat[1] = 0;
mat[2] = 0;
mat[3] = 0;
mat[4] = 0;
mat[5] = 1;
mat[6] = 0;
mat[7] = 0;
mat[8] = 0;
mat[9] = 0;
mat[10] = 1;
mat[11] = 0;
mat[12] = 0;
mat[13] = 0;
mat[14] = 0;
mat[15] = 1;
return mat;
}
Mat4.setIdentity = setIdentity;
function setZero(mat) {
for (var i = 0; i < 16; i++)
mat[i] = 0;
return mat;
}
Mat4.setZero = setZero;
function ofRows(rows) {
var out = zero();
for (var i = 0; i < 4; i++) {
var r = rows[i];
for (var j = 0; j < 4; j++) {
out[4 * j + i] = r[j];
}
}
return out;
}
Mat4.ofRows = ofRows;
var _id = identity();
function isIdentity(m, eps) {
return areEqual(m, _id, typeof eps === 'undefined' ? EPSILON : eps);
}
Mat4.isIdentity = isIdentity;
function hasNaN(m) {
for (var i = 0; i < 16; i++)
if (isNaN(m[i]))
return true;
return false;
}
Mat4.hasNaN = hasNaN;
function areEqual(a, b, eps) {
for (var i = 0; i < 16; i++) {
if (Math.abs(a[i] - b[i]) > eps)
return false;
}
return true;
}
Mat4.areEqual = areEqual;
function setValue(a, i, j, value) {
a[4 * j + i] = value;
}
Mat4.setValue = setValue;
function getValue(a, i, j) {
return a[4 * j + i];
}
Mat4.getValue = getValue;
function toArray(a, out, offset) {
out[offset + 0] = a[0];
out[offset + 1] = a[1];
out[offset + 2] = a[2];
out[offset + 3] = a[3];
out[offset + 4] = a[4];
out[offset + 5] = a[5];
out[offset + 6] = a[6];
out[offset + 7] = a[7];
out[offset + 8] = a[8];
out[offset + 9] = a[9];
out[offset + 10] = a[10];
out[offset + 11] = a[11];
out[offset + 12] = a[12];
out[offset + 13] = a[13];
out[offset + 14] = a[14];
out[offset + 15] = a[15];
return out;
}
Mat4.toArray = toArray;
function fromArray(a, array, offset) {
a[0] = array[offset + 0];
a[1] = array[offset + 1];
a[2] = array[offset + 2];
a[3] = array[offset + 3];
a[4] = array[offset + 4];
a[5] = array[offset + 5];
a[6] = array[offset + 6];
a[7] = array[offset + 7];
a[8] = array[offset + 8];
a[9] = array[offset + 9];
a[10] = array[offset + 10];
a[11] = array[offset + 11];
a[12] = array[offset + 12];
a[13] = array[offset + 13];
a[14] = array[offset + 14];
a[15] = array[offset + 15];
return a;
}
Mat4.fromArray = fromArray;
function fromBasis(a, x, y, z) {
setZero(a);
setValue(a, 0, 0, x[0]);
setValue(a, 1, 0, x[1]);
setValue(a, 2, 0, x[2]);
setValue(a, 0, 1, y[0]);
setValue(a, 1, 1, y[1]);
setValue(a, 2, 1, y[2]);
setValue(a, 0, 2, z[0]);
setValue(a, 1, 2, z[1]);
setValue(a, 2, 2, z[2]);
setValue(a, 3, 3, 1);
return a;
}
Mat4.fromBasis = fromBasis;
function copy(out, a) {
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
out[3] = a[3];
out[4] = a[4];
out[5] = a[5];
out[6] = a[6];
out[7] = a[7];
out[8] = a[8];
out[9] = a[9];
out[10] = a[10];
out[11] = a[11];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
return out;
}
Mat4.copy = copy;
function clone(a) {
return copy(zero(), a);
}
Mat4.clone = clone;
/**
* Returns the translation vector component of a transformation matrix.
*/
function getTranslation(out, mat) {
out[0] = mat[12];
out[1] = mat[13];
out[2] = mat[14];
return out;
}
Mat4.getTranslation = getTranslation;
/**
* Returns the scaling factor component of a transformation matrix.
*/
function getScaling(out, mat) {
var m11 = mat[0];
var m12 = mat[1];
var m13 = mat[2];
var m21 = mat[4];
var m22 = mat[5];
var m23 = mat[6];
var m31 = mat[8];
var m32 = mat[9];
var m33 = mat[10];
out[0] = Math.sqrt(m11 * m11 + m12 * m12 + m13 * m13);
out[1] = Math.sqrt(m21 * m21 + m22 * m22 + m23 * m23);
out[2] = Math.sqrt(m31 * m31 + m32 * m32 + m33 * m33);
return out;
}
Mat4.getScaling = getScaling;
/**
* Returns a quaternion representing the rotational component of a transformation matrix.
*/
function getRotation(out, mat) {
// Algorithm taken from http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
var trace = mat[0] + mat[5] + mat[10];
var S = 0;
if (trace > 0) {
S = Math.sqrt(trace + 1.0) * 2;
out[3] = 0.25 * S;
out[0] = (mat[6] - mat[9]) / S;
out[1] = (mat[8] - mat[2]) / S;
out[2] = (mat[1] - mat[4]) / S;
}
else if ((mat[0] > mat[5]) && (mat[0] > mat[10])) {
S = Math.sqrt(1.0 + mat[0] - mat[5] - mat[10]) * 2;
out[3] = (mat[6] - mat[9]) / S;
out[0] = 0.25 * S;
out[1] = (mat[1] + mat[4]) / S;
out[2] = (mat[8] + mat[2]) / S;
}
else if (mat[5] > mat[10]) {
S = Math.sqrt(1.0 + mat[5] - mat[0] - mat[10]) * 2;
out[3] = (mat[8] - mat[2]) / S;
out[0] = (mat[1] + mat[4]) / S;
out[1] = 0.25 * S;
out[2] = (mat[6] + mat[9]) / S;
}
else {
S = Math.sqrt(1.0 + mat[10] - mat[0] - mat[5]) * 2;
out[3] = (mat[1] - mat[4]) / S;
out[0] = (mat[8] + mat[2]) / S;
out[1] = (mat[6] + mat[9]) / S;
out[2] = 0.25 * S;
}
return out;
}
Mat4.getRotation = getRotation;
function extractRotation(out, mat) {
var scaleX = 1 / Math.sqrt(mat[0] * mat[0] + mat[1] * mat[1] + mat[2] * mat[2]);
var scaleY = 1 / Math.sqrt(mat[4] * mat[4] + mat[5] * mat[5] + mat[6] * mat[6]);
var scaleZ = 1 / Math.sqrt(mat[8] * mat[8] + mat[9] * mat[9] + mat[10] * mat[10]);
out[0] = mat[0] * scaleX;
out[1] = mat[1] * scaleX;
out[2] = mat[2] * scaleX;
out[3] = 0;
out[4] = mat[4] * scaleY;
out[5] = mat[5] * scaleY;
out[6] = mat[6] * scaleY;
out[7] = 0;
out[8] = mat[8] * scaleZ;
out[9] = mat[9] * scaleZ;
out[10] = mat[10] * scaleZ;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
Mat4.extractRotation = extractRotation;
function transpose(out, a) {
// If we are transposing ourselves we can skip a few steps but have to cache some values
if (out === a) {
var a01 = a[1], a02 = a[2], a03 = a[3];
var a12 = a[6], a13 = a[7];
var a23 = a[11];
out[1] = a[4];
out[2] = a[8];
out[3] = a[12];
out[4] = a01;
out[6] = a[9];
out[7] = a[13];
out[8] = a02;
out[9] = a12;
out[11] = a[14];
out[12] = a03;
out[13] = a13;
out[14] = a23;
}
else {
out[0] = a[0];
out[1] = a[4];
out[2] = a[8];
out[3] = a[12];
out[4] = a[1];
out[5] = a[5];
out[6] = a[9];
out[7] = a[13];
out[8] = a[2];
out[9] = a[6];
out[10] = a[10];
out[11] = a[14];
out[12] = a[3];
out[13] = a[7];
out[14] = a[11];
out[15] = a[15];
}
return out;
}
Mat4.transpose = transpose;
function tryInvert(out, a) {
var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3], a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7], a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11], a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15], b00 = a00 * a11 - a01 * a10, b01 = a00 * a12 - a02 * a10, b02 = a00 * a13 - a03 * a10, b03 = a01 * a12 - a02 * a11, b04 = a01 * a13 - a03 * a11, b05 = a02 * a13 - a03 * a12, b06 = a20 * a31 - a21 * a30, b07 = a20 * a32 - a22 * a30, b08 = a20 * a33 - a23 * a30, b09 = a21 * a32 - a22 * a31, b10 = a21 * a33 - a23 * a31, b11 = a22 * a33 - a23 * a32;
// Calculate the determinant
var det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
if (!det) {
return false;
}
det = 1.0 / det;
out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;
return true;
}
Mat4.tryInvert = tryInvert;
function invert(out, a) {
if (!tryInvert(out, a)) {
console.warn('non-invertible matrix.', a);
}
return out;
}
Mat4.invert = invert;
function mul(out, a, b) {
var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3], a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7], a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11], a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
// Cache only the current line of the second matrix
var b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
out[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[4];
b1 = b[5];
b2 = b[6];
b3 = b[7];
out[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[8];
b1 = b[9];
b2 = b[10];
b3 = b[11];
out[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[12];
b1 = b[13];
b2 = b[14];
b3 = b[15];
out[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
return out;
}
Mat4.mul = mul;
/**
* Like `mul` but with offsets into arrays
*/
function mulOffset(out, a, b, oOut, oA, oB) {
var a00 = a[0 + oA], a01 = a[1 + oA], a02 = a[2 + oA], a03 = a[3 + oA], a10 = a[4 + oA], a11 = a[5 + oA], a12 = a[6 + oA], a13 = a[7 + oA], a20 = a[8 + oA], a21 = a[9 + oA], a22 = a[10 + oA], a23 = a[11 + oA], a30 = a[12 + oA], a31 = a[13 + oA], a32 = a[14 + oA], a33 = a[15 + oA];
// Cache only the current line of the second matrix
var b0 = b[0 + oB], b1 = b[1 + oB], b2 = b[2 + oB], b3 = b[3 + oB];
out[0 + oOut] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[1 + oOut] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[2 + oOut] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[3 + oOut] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[4 + oB];
b1 = b[5 + oB];
b2 = b[6 + oB];
b3 = b[7 + oB];
out[4 + oOut] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[5 + oOut] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[6 + oOut] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[7 + oOut] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[8 + oB];
b1 = b[9 + oB];
b2 = b[10 + oB];
b3 = b[11 + oB];
out[8 + oOut] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[9 + oOut] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[10 + oOut] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[11 + oOut] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[12 + oB];
b1 = b[13 + oB];
b2 = b[14 + oB];
b3 = b[15 + oB];
out[12 + oOut] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[13 + oOut] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[14 + oOut] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[15 + oOut] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
return out;
}
Mat4.mulOffset = mulOffset;
function mul3(out, a, b, c) {
return mul(out, mul(out, a, b), c);
}
Mat4.mul3 = mul3;
/** Translate a Mat4 by the given Vec3 */
function translate(out, a, v) {
var x = v[0], y = v[1], z = v[2];
var a00, a01, a02, a03, a10, a11, a12, a13, a20, a21, a22, a23;
if (a === out) {
out[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
out[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
out[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
out[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
}
else {
a00 = a[0];
a01 = a[1];
a02 = a[2];
a03 = a[3];
a10 = a[4];
a11 = a[5];
a12 = a[6];
a13 = a[7];
a20 = a[8];
a21 = a[9];
a22 = a[10];
a23 = a[11];
out[0] = a00;
out[1] = a01;
out[2] = a02;
out[3] = a03;
out[4] = a10;
out[5] = a11;
out[6] = a12;
out[7] = a13;
out[8] = a20;
out[9] = a21;
out[10] = a22;
out[11] = a23;
out[12] = a00 * x + a10 * y + a20 * z + a[12];
out[13] = a01 * x + a11 * y + a21 * z + a[13];
out[14] = a02 * x + a12 * y + a22 * z + a[14];
out[15] = a03 * x + a13 * y + a23 * z + a[15];
}
return out;
}
Mat4.translate = translate;
function fromTranslation(out, v) {
out[0] = 1;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = 1;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 1;
out[11] = 0;
out[12] = v[0];
out[13] = v[1];
out[14] = v[2];
out[15] = 1;
return out;
}
Mat4.fromTranslation = fromTranslation;
function setTranslation(out, v) {
out[12] = v[0];
out[13] = v[1];
out[14] = v[2];
return out;
}
Mat4.setTranslation = setTranslation;
/**
* Sets the specified quaternion with values corresponding to the given
* axes. Each axis is a vec3 and is expected to be unit length and
* perpendicular to all other specified axes.
*/
function setAxes(out, view, right, up) {
out[0] = right[0];
out[4] = right[1];
out[8] = right[2];
out[1] = up[0];
out[5] = up[1];
out[9] = up[2];
out[2] = view[0];
out[6] = view[1];
out[10] = view[2];
return out;
}
Mat4.setAxes = setAxes;
function rotate(out, a, rad, axis) {
var x = axis[0], y = axis[1], z = axis[2];
var len = Math.sqrt(x * x + y * y + z * z);
if (Math.abs(len) < EPSILON) {
return identity();
}
len = 1 / len;
x *= len;
y *= len;
z *= len;
var s = Math.sin(rad);
var c = Math.cos(rad);
var t = 1 - c;
var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
var a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
var a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
// Construct the elements of the rotation matrix
var b00 = x * x * t + c, b01 = y * x * t + z * s, b02 = z * x * t - y * s;
var b10 = x * y * t - z * s, b11 = y * y * t + c, b12 = z * y * t + x * s;
var b20 = x * z * t + y * s, b21 = y * z * t - x * s, b22 = z * z * t + c;
// Perform rotation-specific matrix multiplication
out[0] = a00 * b00 + a10 * b01 + a20 * b02;
out[1] = a01 * b00 + a11 * b01 + a21 * b02;
out[2] = a02 * b00 + a12 * b01 + a22 * b02;
out[3] = a03 * b00 + a13 * b01 + a23 * b02;
out[4] = a00 * b10 + a10 * b11 + a20 * b12;
out[5] = a01 * b10 + a11 * b11 + a21 * b12;
out[6] = a02 * b10 + a12 * b11 + a22 * b12;
out[7] = a03 * b10 + a13 * b11 + a23 * b12;
out[8] = a00 * b20 + a10 * b21 + a20 * b22;
out[9] = a01 * b20 + a11 * b21 + a21 * b22;
out[10] = a02 * b20 + a12 * b21 + a22 * b22;
out[11] = a03 * b20 + a13 * b21 + a23 * b22;
if (a !== out) { // If the source and destination differ, copy the unchanged last row
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
}
return out;
}
Mat4.rotate = rotate;
function fromRotation(out, rad, axis) {
var x = axis[0], y = axis[1], z = axis[2];
var len = Math.sqrt(x * x + y * y + z * z);
if (Math.abs(len) < EPSILON) {
return setIdentity(out);
}
len = 1 / len;
x *= len;
y *= len;
z *= len;
var s = Math.sin(rad);
var c = Math.cos(rad);
var t = 1 - c;
// Perform rotation-specific matrix multiplication
out[0] = x * x * t + c;
out[1] = y * x * t + z * s;
out[2] = z * x * t - y * s;
out[3] = 0;
out[4] = x * y * t - z * s;
out[5] = y * y * t + c;
out[6] = z * y * t + x * s;
out[7] = 0;
out[8] = x * z * t + y * s;
out[9] = y * z * t - x * s;
out[10] = z * z * t + c;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
Mat4.fromRotation = fromRotation;
function scale(out, a, v) {
var x = v[0], y = v[1], z = v[2];
out[0] = a[0] * x;
out[1] = a[1] * x;
out[2] = a[2] * x;
out[3] = a[3] * x;
out[4] = a[4] * y;
out[5] = a[5] * y;
out[6] = a[6] * y;
out[7] = a[7] * y;
out[8] = a[8] * z;
out[9] = a[9] * z;
out[10] = a[10] * z;
out[11] = a[11] * z;
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
return out;
}
Mat4.scale = scale;
function scaleUniformly(out, a, scale) {
out[0] = a[0] * scale;
out[1] = a[1] * scale;
out[2] = a[2] * scale;
out[3] = a[3] * scale;
out[4] = a[4] * scale;
out[5] = a[5] * scale;
out[6] = a[6] * scale;
out[7] = a[7] * scale;
out[8] = a[8] * scale;
out[9] = a[9] * scale;
out[10] = a[10] * scale;
out[11] = a[11] * scale;
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
return out;
}
Mat4.scaleUniformly = scaleUniformly;
function fromScaling(out, v) {
out[0] = v[0];
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = v[1];
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = v[2];
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
Mat4.fromScaling = fromScaling;
function fromUniformScaling(out, scale) {
out[0] = scale;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = scale;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = scale;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
Mat4.fromUniformScaling = fromUniformScaling;
/**
* Copies the mat3 into upper-left 3x3 values.
*/
function fromMat3(out, a) {
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
out[4] = a[3];
out[5] = a[4];
out[6] = a[5];
out[8] = a[6];
out[9] = a[7];
out[10] = a[8];
return out;
}
Mat4.fromMat3 = fromMat3;
function makeTable(m) {
var ret = '';
for (var i = 0; i < 4; i++) {
for (var j = 0; j < 4; j++) {
ret += m[4 * j + i].toString();
if (j < 3)
ret += ' ';
}
if (i < 3)
ret += '\n';
}
return ret;
}
Mat4.makeTable = makeTable;
function determinant(a) {
var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3], a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7], a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11], a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15], b00 = a00 * a11 - a01 * a10, b01 = a00 * a12 - a02 * a10, b02 = a00 * a13 - a03 * a10, b03 = a01 * a12 - a02 * a11, b04 = a01 * a13 - a03 * a11, b05 = a02 * a13 - a03 * a12, b06 = a20 * a31 - a21 * a30, b07 = a20 * a32 - a22 * a30, b08 = a20 * a33 - a23 * a30, b09 = a21 * a32 - a22 * a31, b10 = a21 * a33 - a23 * a31, b11 = a22 * a33 - a23 * a32;
// Calculate the determinant
return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
}
Mat4.determinant = determinant;
/**
* Check if the matrix has the form
* [ Rotation Translation ]
* [ 0 1 ]
*
* Allows for improper rotations
*/
function isRotationAndTranslation(a, eps) {
return _isRotationAndTranslation(a, typeof eps !== 'undefined' ? eps : EPSILON);
}
Mat4.isRotationAndTranslation = isRotationAndTranslation;
function _isRotationAndTranslation(a, eps) {
var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3], a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7], a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11], a33 = a[15];
if (!equalEps(a33, 1, eps) || !equalEps(a03, 0, eps) || !equalEps(a13, 0, eps) || !equalEps(a23, 0, eps)) {
return false;
}
// use `abs` to allow for improper rotations
var det3x3 = Math.abs(a00 * (a11 * a22 - a12 * a21) - a01 * (a10 * a22 - a12 * a20) + a02 * (a10 * a21 - a11 * a20));
if (!equalEps(det3x3, 1, eps)) {
return false;
}
return true;
}
/**
* Check if the matrix has only translation and uniform scaling
* [ S 0 0 X ]
* [ 0 S 0 Y ]
* [ 0 0 S Z ]
* [ 0 0 0 1 ]
*/
function isTranslationAndUniformScaling(a, eps) {
return _isTranslationAndUniformScaling(a, typeof eps !== 'undefined' ? eps : EPSILON);
}
Mat4.isTranslationAndUniformScaling = isTranslationAndUniformScaling;
function _isTranslationAndUniformScaling(a, eps) {
var a00 = a[0];
return (
// 0 base scaling
equalEps(a[1], 0, eps) &&
equalEps(a[2], 0, eps) &&
equalEps(a[3], 0, eps) &&
equalEps(a[4], 0, eps) &&
equalEps(a[5], a00, eps) &&
equalEps(a[6], 0, eps) &&
equalEps(a[7], 0, eps) &&
equalEps(a[8], 0, eps) &&
equalEps(a[9], 0, eps) &&
equalEps(a[10], a00, eps) &&
equalEps(a[11], 0, eps) &&
// 12, 13, 14 translation can be anything
equalEps(a[15], 1, eps));
}
function fromQuat(out, q) {
var x = q[0], y = q[1], z = q[2], w = q[3];
var x2 = x + x;
var y2 = y + y;
var z2 = z + z;
var xx = x * x2;
var yx = y * x2;
var yy = y * y2;
var zx = z * x2;
var zy = z * y2;
var zz = z * z2;
var wx = w * x2;
var wy = w * y2;
var wz = w * z2;
out[0] = 1 - yy - zz;
out[1] = yx + wz;
out[2] = zx - wy;
out[3] = 0;
out[4] = yx - wz;
out[5] = 1 - xx - zz;
out[6] = zy + wx;
out[7] = 0;
out[8] = zx + wy;
out[9] = zy - wx;
out[10] = 1 - xx - yy;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
Mat4.fromQuat = fromQuat;
/**
* Generates a perspective projection (frustum) matrix with the given bounds
*/
function perspective(out, left, right, top, bottom, near, far) {
var x = 2 * near / (right - left);
var y = 2 * near / (top - bottom);
var a = (right + left) / (right - left);
var b = (top + bottom) / (top - bottom);
var c = -(far + near) / (far - near);
var d = -2 * far * near / (far - near);
out[0] = x;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = y;
out[6] = 0;
out[7] = 0;
out[8] = a;
out[9] = b;
out[10] = c;
out[11] = -1;
out[12] = 0;
out[13] = 0;
out[14] = d;
out[15] = 0;
return out;
}
Mat4.perspective = perspective;
/**
* Generates a orthogonal projection matrix with the given bounds
*/
function ortho(out, left, right, top, bottom, near, far) {
var w = 1.0 / (right - left);
var h = 1.0 / (top - bottom);
var p = 1.0 / (far - near);
var x = (right + left) * w;
var y = (top + bottom) * h;
var z = (far + near) * p;
out[0] = 2 * w;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = 2 * h;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = -2 * p;
out[11] = 0;
out[12] = -x;
out[13] = -y;
out[14] = -z;
out[15] = 1;
return out;
}
Mat4.ortho = ortho;
/**
* Generates a look-at matrix with the given eye position, focal point, and up axis
*/
function lookAt(out, eye, center, up) {
var x0, x1, x2, y0, y1, y2, z0, z1, z2, len;
var eyex = eye[0];
var eyey = eye[1];
var eyez = eye[2];
var upx = up[0];
var upy = up[1];
var upz = up[2];
var centerx = center[0];
var centery = center[1];
var centerz = center[2];
if (Math.abs(eyex - centerx) < EPSILON &&
Math.abs(eyey - centery) < EPSILON &&
Math.abs(eyez - centerz) < EPSILON) {
return setIdentity(out);
}
z0 = eyex - centerx;
z1 = eyey - centery;
z2 = eyez - centerz;
len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
z0 *= len;
z1 *= len;
z2 *= len;
x0 = upy * z2 - upz * z1;
x1 = upz * z0 - upx * z2;
x2 = upx * z1 - upy * z0;
len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2);
if (!len) {
x0 = 0;
x1 = 0;
x2 = 0;
}
else {
len = 1 / len;
x0 *= len;
x1 *= len;
x2 *= len;
}
y0 = z1 * x2 - z2 * x1;
y1 = z2 * x0 - z0 * x2;
y2 = z0 * x1 - z1 * x0;
len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2);
if (!len) {
y0 = 0;
y1 = 0;
y2 = 0;
}
else {
len = 1 / len;
y0 *= len;
y1 *= len;
y2 *= len;
}
out[0] = x0;
out[1] = y0;
out[2] = z0;
out[3] = 0;
out[4] = x1;
out[5] = y1;
out[6] = z1;
out[7] = 0;
out[8] = x2;
out[9] = y2;
out[10] = z2;
out[11] = 0;
out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
out[15] = 1;
return out;
}
Mat4.lookAt = lookAt;
/**
* Generates a matrix that makes something look at something else.
*/
function targetTo(out, eye, target, up) {
var eyex = eye[0], eyey = eye[1], eyez = eye[2], upx = up[0], upy = up[1], upz = up[2];
var z0 = eyex - target[0], z1 = eyey - target[1], z2 = eyez - target[2];
var len = z0 * z0 + z1 * z1 + z2 * z2;
if (len > 0) {
len = 1 / Math.sqrt(len);
z0 *= len;
z1 *= len;
z2 *= len;
}
var x0 = upy * z2 - upz * z1, x1 = upz * z0 - upx * z2, x2 = upx * z1 - upy * z0;
len = x0 * x0 + x1 * x1 + x2 * x2;
if (len > 0) {
len = 1 / Math.sqrt(len);
x0 *= len;
x1 *= len;
x2 *= len;
}
out[0] = x0;
out[1] = x1;
out[2] = x2;
out[3] = 0;
out[4] = z1 * x2 - z2 * x1;
out[5] = z2 * x0 - z0 * x2;
out[6] = z0 * x1 - z1 * x0;
out[7] = 0;
out[8] = z0;
out[9] = z1;
out[10] = z2;
out[11] = 0;
out[12] = eyex;
out[13] = eyey;
out[14] = eyez;
out[15] = 1;
return out;
}
Mat4.targetTo = targetTo;
/**
* Perm is 0-indexed permutation
*/
function fromPermutation(out, perm) {
setZero(out);
for (var i = 0; i < 4; i++) {
var p = perm[i];
setValue(out, i, p, 1);
}
return out;
}
Mat4.fromPermutation = fromPermutation;
function getMaxScaleOnAxis(m) {
var scaleXSq = m[0] * m[0] + m[1] * m[1] + m[2] * m[2];
var scaleYSq = m[4] * m[4] + m[5] * m[5] + m[6] * m[6];
var scaleZSq = m[8] * m[8] + m[9] * m[9] + m[10] * m[10];
return Math.sqrt(Math.max(scaleXSq, scaleYSq, scaleZSq));
}
Mat4.getMaxScaleOnAxis = getMaxScaleOnAxis;
var xAxis = [1, 0, 0];
var yAxis = [0, 1, 0];
var zAxis = [0, 0, 1];
/** Rotation matrix for 90deg around x-axis */
Mat4.rotX90 = fromRotation(zero(), degToRad(90), xAxis);
/** Rotation matrix for 180deg around x-axis */
Mat4.rotX180 = fromRotation(zero(), degToRad(180), xAxis);
/** Rotation matrix for 90deg around y-axis */
Mat4.rotY90 = fromRotation(zero(), degToRad(90), yAxis);
/** Rotation matrix for 180deg around y-axis */
Mat4.rotY180 = fromRotation(zero(), degToRad(180), yAxis);
/** Rotation matrix for 270deg around y-axis */
Mat4.rotY270 = fromRotation(zero(), degToRad(270), yAxis);
/** Rotation matrix for 90deg around z-axis */
Mat4.rotZ90 = fromRotation(zero(), degToRad(90), zAxis);
/** Rotation matrix for 180deg around z-axis */
Mat4.rotZ180 = fromRotation(zero(), degToRad(180), zAxis);
/** Rotation matrix for 90deg around first x-axis and then y-axis */
Mat4.rotXY90 = mul(zero(), Mat4.rotX90, Mat4.rotY90);
/** Rotation matrix for 90deg around first z-axis and then y-axis */
Mat4.rotZY90 = mul(zero(), Mat4.rotZ90, Mat4.rotY90);
/** Rotation matrix for 90deg around first z-axis and then y-axis and then z-axis */
Mat4.rotZYZ90 = mul(zero(), Mat4.rotZY90, Mat4.rotZ90);
/** Rotation matrix for 90deg around first z-axis and then 180deg around x-axis */
Mat4.rotZ90X180 = mul(zero(), Mat4.rotZ90, Mat4.rotX180);
/** Rotation matrix for 90deg around first y-axis and then 180deg around z-axis */
Mat4.rotY90Z180 = mul(zero(), Mat4.rotY90, Mat4.rotZ180);
/** Identity matrix */
Mat4.id = identity();
})(Mat4 || (Mat4 = {}));
export { Mat4 };
//# sourceMappingURL=mat4.js.map